7. A game involves selecting a card from a regular 52-card deck and tossing a coin. The coin is a fair coin and is equally likely to land on heads or tails.

	If the card is a face card, and the coin lands on Heads, you win $4
	If the card is a face card, and the coin lands on Tails, you win $1
	If the card is not a face card, you lose $1, no matter what the coin shows.

(a)Find the expected value for this game (expected net gain or loss). (Round your answer to two decimal places.) $ ______

(b)Explain what your calculations indicate about your long-term average profits and losses on this game.

a. The calculated value represents a fixed amount that your total money will change after each loss.

b. The calculated value represents a fixed amount that your total money will change after each game.

c. The calculated value represents the average amount per game that your total money will change over a large number of games.

d. The calculated value represents the average amount per loss that your total money will change over a large number of games.

(c)Should you play this game to win money?

a. Yes, because the expected value indicates an expected average gain.

b. No, because the expected value indicates an expected average loss.

8. At The Fencing Center, 60% of the fencers use the foil as their main weapon. We randomly survey 20 fencers at The Fencing Center. We are interested in the numbers that do not use the foil as their main weapon.

(a)In words, define the Random VariableX.

a. the different types of weapons

b. the number of fencers that do use the foil as their main weapon

c. the number of fencers at The Fencing Center

d. the number of fencers that do not use the foil as their main weapon

(b)List the values thatXmay take on.

a. X= 1, 2, 3, . . ., 60

b. X= 1, 2, 3, . . ., 20

c. X= 0, 1, 2, . . ., 20

d. X= 0, 1, 2, . . ., 60

(c)Give the distribution ofX. X~ ____ ( ____ , ____ )

(d)How many fencers are expected tonotuse the foil as their main weapon? (Round your answer to the nearest whole number.) _______ fencers

(e)Find the probability that six donotuse the foil as their main weapon. (Round your answer to four decimal places.)

(f)Based on numerical values, would you be surprised if all 20 didnotuse foil as their main weapon?

a. Yes. The probability of all 20 fencers not using the foil as their main weapon is small (less than 1%).

b. No. The probability of all 20 fencers not using the foil as their main weapon is large (more than 10%).